Lagrangian Integral Time Scale Research Articles

Surface drifter derived circulation in the northern and middle Adriatic Sea: Response to wind regime and season

More than 120 satellite‐tracked drifters were deployed in the northern and middle Adriatic (NMA) Sea between September 2002 and November 2003, with the purpose of studying the surface circulation at mesoscale to seasonal scale in relation to wind forcing, river runoff, and bottom topography. Pseudo‐Eulerian and Lagrangian statistics were calculated from the low‐pass‐filtered drifter velocity data between September 2002 and December 2003. The structure of the mean circulation is determined with unprecedented high horizontal resolution by the new data. In particular, mean currents, velocity variance, and kinetic energy levels are shown to be maximal in the Western Adriatic Current (WAC). Separating data into seasons, we found that the mean kinetic energy is maximal in fall, with high values also in winter, while it is significantly weaker in summer. High‐resolution Local Area Model Italy winds were used to relate the drifter velocities to the wind fields. The surface currents appear to be significantly influenced by the winds. The mean flow during the northeasterly bora regime shows an intensification of the across‐basin recirculating currents. In addition, the WAC is strongly intensified both in intensity and in its offshore lateral extension. In the southeasterly sirocco regime, northward flow without recirculation dominates in the eastern half of the basin, while during northwesterly maestro the WAC is enhanced. Separating the data into low and high Po River discharge rates for low‐wind conditions shows that the WAC and the velocity fluctuations in front of the Po delta are stronger for high Po River runoff. Lagrangian covariance, diffusivity, and integral time and space scales are larger in the along‐basin direction and are maximal in the southern portion of the WAC.

Reynolds number dependence of Lagrangian statistics in large numerical simulations of isotropic turbulence

Lagrangian statistics are reported from a direct numerical simulation database with grid resolution up to 20483 and Taylor-scale Reynolds number approximately 650. The approach to Lagrangian Kolmogorov similarity at high Reynolds number is studied using both the velocity structure function and frequency spectrum. A significant scaling range is observed for the latter which is consistent with recent estimates of 6–7 for the scaling constant C 0. In contrast to some previous results at low Reynolds number, the current results suggest that at high Reynolds number the dissipation autocorrelation is a two-scale process influenced by both the Lagrangian velocity integral time scale and Kolmogorov time scale. Results on the logarithm of the pseudo-dissipation are in support of its modeling as a diffusion process with one-time Gaussian statistics. As the Reynolds number increases, the statistics of dissipation and enstrophy become more similar while their logarithms have significantly longer time scales.

Lagrangian Observations of the Middepth and Deep Velocity Fields of the Northeastern Atlantic Ocean

Abstract The circulation of the northeastern Atlantic Ocean at intermediate depths is characterized by watermass transformation processes that involve Iceland–Scotland Overflow Water (ISOW) from the northeast, Labrador Sea Water (LSW) from the west, and Mediterranean Water from the south. Field observations were carried out with 89 eddy-resolving floats (RAFOS and MARVOR types). The data coverage achieved is remarkably high and enables a comprehensive study of the eastern basins between Iceland and the Azores. The trajectories show typical pathways of the water masses involved and the role that the complex bottom topography plays in defining them. The ISOW paths tend to lean against the slopes of the Reykjanes Ridge and Rockall Plateau. Westward escapes through multiple gaps in the ridge are possible, superimposed on a sustained southward flow in the eastern basin along the Mid-Atlantic Ridge. LSW pathways leading to the eastern basins are subject to high variability in flow direction and eddy activity. In addition to a selection of characteristic trajectories, maps of the horizontal distributions of Lagrangian eddy kinetic energy and integral time scales are presented. These reveal distinct areas of intensified mixing in the Iceland Basin, as well as the sharp contrast between the subpolar and subtropical dynamics. A self-contained eddy detection scheme is applied to obtain statistics on individual eddy properties and their abundance. It is suggested that much of the intensified mixing can be related to cyclonic activity, particularly in the subpolar region.

Statistical description of the Black Sea near-surface circulation using drifters in 1999–2003

The near-surface circulation in the Black Sea is studied with the data of 54 satellite-tracked drifters in the period 1999–2003. The drifter trajectories confirm the prevalence of the Rim Current trapped on the continental slope (between water depths of 400 and 1800 m) along the periphery of the basin where sub-inertial speeds can reach 1 m/s. Some drifters were found to complete an entire basin loop with the Rim Current in 90–180 days. Meanders and loops in the tracks prove the existence of mostly anticyclonic circulation features inshore of the Rim Current, including strong signatures of the Batumi and Sevastopol eddies. They also reveal the presence of cyclonic and anticyclonic currents in most areas of the Black Sea. Pseudo-Eulerian statistics (averaged in 50-km bins), that is, mean currents and the corresponding velocity variances, show a strong and highly fluctuating signature of the Rim Current and the enhanced variability associated with the Batumi and Sevastopol eddies. The latter is also collocated with the branching of the Rim Current southwest of the Crimean Peninsula. It is shown that the kinetic energy is mainly in the mean for the Rim Current and in the velocity fluctuations elsewhere. Seasonal variability is also explored. The Rim Current tends to form a stronger single loop trapped on the continental slope in winter/spring, whereas in summer/fall the mean circulation is more meandering, recirculation cells appear in the central areas and the bifurcation southwest of Crimea is enhanced. There is some evidence of the reversal of sense of rotation of the currents in the Batumi Eddy region, changing from mainly anticyclonic in summer/fall to cyclonic in winter/spring. Mean residence times were calculated in the 50-km bins, with values ranging from a few days in the central basin to 8 days in the northwestern coastal area. Globally, the kinetic energy levels were found higher in winter–spring and lower in summer–fall, with a significant maximum in March. Single-particle Lagrangian statistics were computed for the entire basin, for the two extended seasons, and in selected local areas. Velocity variance, diffusivity and Lagrangian integral time scales are generally larger in the zonal direction. Globally, the velocity variance is 174 and 127 cm 2/s 2 in the zonal and meridional directions, respectively, after the removal of the pseudo-Eulerian mean circulation. For the zonal direction, a diffusivity value of 4.5×10 7 cm 2/s and Lagrangian integral time and space scales of 3 days and 34 km were found. For the meridional direction, these statistics amount to 4.5×10 7 cm 2/s, 1.2 days and 12.2 km. Seasonal and geographical variations of these Lagrangian statistics were also assessed, showing variations between 1.9 (0.9) 10 7 and 8.3 (2.0) 10 7 cm 2/s for the diffusivity in the zonal (meridional) direction. Integral time and space scales vary between 1 and 4.7 days, and 8.8 and 58 km, respectively. Seasonal differences are significant only in the zonal direction, where the diffusivity increases from 3.1×10 7 to 5.9×10 7 cm 2/s and the integral scales vary from 2.1 days (24 km) to 3.8 days (44 km) from summer/fall to winter/spring.

Particle behavior in homogeneous isotropic turbulence

Direct numerical simulations were conducted to investigate the behavior of heavy particles in homogeneous isotropic turbulence. The present study focused on the effect of particle inertia and drift on the autocorrelations of the particle velocity and the fluid seen by particles and the dispersion characteristics of particles. The Lagrangian integral time scale of particles monotonically increased as the magnitude of the particle response time increased, while that of the fluid seen by particles remained relatively constant; it reached a maximum when the particle response time was close to the Kolmolgorov time scale of the flow. Particle dispersion increased as the particle inertia increased for small particles, while for larger particles, it decreased as particle inertia increased; particle eddy diffusion coefficient was maximal, and greater than that of the fluid by about 30%, at the preferential concentration. The concentration field of the particles with τp/τk≈1.0 showed that particles tend to collect in regions of low vorticity (high strain) due to preferential concentration. As the drift velocity of a particle is increased it crosses the paths of fluid elements more rapidly and will tend to lose correlation with its previous velocity faster than a fluid element will. And the correlation of particle velocities along the drift direction is more persistent than that perpendicular to the direction of drift. Simulations also showed that the continuity effect and the crossing-trajectory effect are weakened for particles with infinite inertia.

The mid-depth circulation of the subpolar North Atlantic Ocean as measured by subsurface floats

The multi-year mean, mid-depth circulation of the subpolar North Atlantic Ocean was estimated from direct velocity measurements obtained over a 7.5-year period by 211 neutrally-buoyant, profiling, subsurface floats. We present a statistical analysis of these drift velocity data, and describe the features of the circulation from 400–1500 m depth as measured by the floats. The time-lagged auto-covariances of velocity indicate a Lagrangian integral time scale of approximately 10 days at all drift depths and throughout the basin. Space–time averages of velocity and the associated error ellipses were constructed, and this information was used in an objective analysis to produce estimates of the multi-year mean flow. Estimates of eddy kinetic energy were also computed. The mapped flow depicts a basin-scale cyclonic gyre bounded in the south by the North Atlantic Current. The strongest currents are found along the coasts of Greenland and Labrador, where mean speeds exceed 10 cm s - 1 . Closed cyclonic recirculations appear just offshore of the boundary currents in the Labrador and Irminger Seas and in the Iceland basin, and also southwest of the Reykjanes Ridge. Topographic steering extends upwards to at least 400 m depth above bathymetry that is significantly deeper, and is most apparent in flow along basin boundaries, around the Reykjanes Ridge, and through gaps in the Mid-Atlantic Ridge. In the center of the basin-scale gyre and to the south of the North Atlantic Current flow is characteristically weak with few large-scale circulation features. There is no indication of a strong linkage along the western boundary from the subpolar to subtropical gyre at depths sampled by floats.

Revised estimates for continuous shoreline fumigation: a PDF approach

A probability density function (PDF) fumigation model is presented here to study the dispersion of air pollutants emitted from a tall stack on the shoreline. This work considers dispersion of the pollutants in the stable layer and within the thermal internal boundary layer (TIBL) proceeds independently. The growth of TIBL is considered parabolic with distance inland. Turbulence is taken as homogeneous and stationary. Dispersion of particles (contaminant) in lateral and vertical directions is assumed independent of each other. This assumption allows us to consider the position of particles in both directions as independent random variables. The lateral dispersion distribution within the TIBL is considered as Gaussian and independent of height. A skewed bi-Gaussian vertical velocity PDF is used to account for the physics of dispersion due to different characteristics of updrafts and downdrafts within the TIBL. We have used Weil (J.C. Weil, A diagnosis of the asymmetry in top-down and bottom-up diffusion using a Lagrangian stochastic model, J. Atmos. Sci., 47 (1990) 501–515) solutions to find out the parameters of this PDF. Incorporating finite Lagrangian integral time scale for the vertical velocity component, it is observed that it reduces the vertical dispersion in the beginning and moves the point of maximum concentration further downwind. Due to little dispersion in the beginning, there is more plume to be dispersed causing higher concentrations at large distances. The model has considered Weil and Brower's (J.C. Weil, P.R. Brower, Estimating convective boundary layer parameters for diffusion applications, Maryland Power Plant Siting Program Rep. PPSP-MP-48, Department of Natural Resources, Annapolis, MD, 1985, 37 pp.) convective limit to analyze dispersion characteristics within TIBL. The revised model discussed here is evaluated with the data available from the Nanticoke field experiment on fumigation conducted in summer of 1978 in Ontario, Canada. The results of revised model are in good agreement with the observed data.

Development and Characterization of Jet-Injected Vee-Gutter

ABSTRACTThe vee-gutter, which was conventionally used in a combustor for flame holding, was re-designed by employing the unsteady Coanda effect to inject fluids periodically into near wake of the vee-gutter. Fluidic targets were developed to induce self-sustained transverse oscillation of slit-jet. The self-sustained oscillating jet was conducted through passages and injected into the near wake of the vee-gutter. The behaviors and frequency characteristics of the slit-jet in the oscillation cavity and the turbulence properties in the wake were studied experimentally in a wind-tunnel by using the smoke-wire flow visualization technique and the hot-wire anemometer. The oscillation frequencies of the presently developed jet-injection vee-gutter were about 25 to 40 times higher than that of the conventionally used fluidic flowmeter. By estimating the Lagrangian integral time scale and employing the Taylor's frozen flow hypothesis, the integral length scales of turbulence fluctuations were calculated. The results showed that the integral length scales of turbulences of the jet-injected vee-gutter were significantly smaller than their counter parts of the conventional vee-gutter, which indicated the effects of vortex stretching induced by the periodic jet injection. The modifications of turbulence properties were presented and discussed.

Lagrangian statistics in turbulent channel flow

The Lagrangian dispersion of fluid particles in inhomogeneous turbulence is investigated by a direct numerical simulation of turbulent channel flow. Lagrangian velocity and acceleration along a particle trajectory are computed by employing several interpolation schemes. Among the schemes tested, the four-point Hermite interpolation in the homogeneous directions combined with Chebyshev polynomials in the wall-normal direction seems to produce most reliable Lagrangian statistics. Inhomogeneity of Lagrangian statistics in turbulent boundary layer is investigated by releasing many particles at several different wall-normal locations and tracking those particles. The fluid particle dispersion and Lagrangian structure function of velocity are investigated for the Kolmogorov similarity. The behavior of the Lagrangian integral time scales, Kolmogorov constants a0 and C0 of the velocity structure function near the wall are discussed. The intermittent behavior of the fluid particle acceleration is also examined by kurtosis of the Lagrangian structure function. Finally, the effect of the initial particle location on the dispersion is analyzed by the probability density function of particle position at several downstream locations.

Improved Lagrangian mixing models for passive scalars in isotropic turbulence

Lagrangian data for velocity, scalars, and energy and scalar dissipation from direct numerical simulations are used to validate Lagrangian mixing models for inert passive scalars in stationary isotropic turbulence. The scalar fluctuations are nearly Gaussian, and, as a result of production by uniform mean gradients, statistically stationary. Comparisons are made for Taylor-scale Reynolds numbers in the range 38 to about 240 and Schmidt numbers in the range 1/8 to 1. Model predictions for one-point, one-time Eulerian statistics (Eulerian correspondence) and one-particle, two-time Lagrangian statistics (Lagrangian correspondence) are examined. Two scalar mixing models, namely the Lagrangian Fokker–Planck model and the Lagrangian colored-noise (LCN) model, are proposed and written in terms of stochastic differential equations (SDE) with specified drift and diffusion terms. Both of these models rely on statistics of the scalar field conditioned upon the energy dissipation, as provided by the Lagrangian spectral relaxation (LSR) model. With the exception of the scalar dissipation, the models are shown to capture the Reynolds and Schmidt-number dependence of the Lagrangian integral time scales. However, the LCN model provides a more realistic description of the Lagrangian scalar fluctuations as differentiable time series having the correct form of the scalar autocorrelation function. Further extensions of the new mixing models to non-Gaussian scalars are conceptually straightforward, but require a closure for the scalar-conditioned scalar dissipation rate matrix. Likewise, accurate prediction of joint statistics for differential diffusion between different scalars with unequal molecular diffusivities will require the formulation of a multiscale SDE similar to the LSR model.

Assimilation of drifter observations for the reconstruction of the Eulerian circulation field

In light of the increasing number of drifting buoys in the ocean and recent advances in the realism of ocean general circulation models toward oceanic forecasting, the problem of assimilation of Lagrangian observations data in Eulerian models is investigated. A new and general rigorous approach is developed based on optimal interpolation (OI) methods, which takes into account directly the Lagrangian nature of the observations. An idealized version of this general formulation is tested in the framework of identical twin experiments using a reduced gravity, quasi‐geostrophic model. An extensive study is conducted to quantify the effectiveness of Lagrangian data assimilation as a function of the number of drifters, the frequency of assimilation, and the uncertainties associated with the forcing functions driving the ocean model. The performance of the Lagrangian assimilation technique is also compared to that of conventional methods of assimilating drifters as moving current meters, and assimilation of Eulerian data, such as fixed‐point velocities. Overall, the results are very favorable for the assimilation of Lagrangian observations to improve the Eulerian velocity field in ocean models. The results of our assimilation twin experiments imply an optimal sampling frequency for oceanic Lagrangian instruments in the range of 20–50% of the Lagrangian integral timescale of the flow field.

The motion of fibres in turbulent flow, stochastic simulation of isotropic homogeneous turbulence

The state of fibres suspended in a turbulent fluid is described in terms of a probability distribution function of fibre orientation and position throughout the suspending fluid. The evolution of the fibre's probability distribution function is governed by a convection–dispersion equation, where the randomizing effect of the turbulence is modelled by rotational and translational dispersion coefficients. To estimate these coefficients a numerical simulation of fibres moving in a turbulent fluid was developed. The trajectory of an ensemble of inertialess, rigid, thin, free-draining fibres was calculated through a stochastic model of homogeneous, isotropic turbulence. The results of the simulation were compared with analytical estimates and were found to provide reasonable agreement over a wide range of fibre length. However, the simulation showed that the Lagrangian integral time scale for rotation was significantly smaller than for translation and the ratio of rotational to translational Lagrangian time scales was smaller than the ratio of Eulerian time scales. The simulation also showed that the Lagrangian velocity correlation increased as fibre length increased and that the temporal correlations approached the analytical estimates of the Eulerian correlations in the limit of long fibres.

Adriatic Sea surface circulation as derived from drifter data between 1990 and 1999

The Adriatic Sea surface circulation for the period 1990–1999 is studied using the data of more than 200 satellite-tracked drifters. The spatial structure and the temporal variability of the surface currents, at meso- to seasonal scales, are described in terms of Eulerian and Lagrangian statistics estimated from the low-pass filtered drifter velocities. Maps of mean currents, subtidal velocity variance and mean kinetic energies were produced using a 40-km averaging scale. The mean flow map confirms that the global cyclonic circulation in most of the Adriatic basin is broken into three re-circulation cells in the northern, central and southern sub-basins (the latter two being controlled by the bathymetry of the Jabuka and South Adriatic Pits, respectively). An isolated cyclonic gyre prevails near the head of the basin. Mean velocities in the cyclonic gyres can exceed 25 cm s −1 in the coastal areas where the velocity variance is also maximum (reaching 500 cm 2 s −2). Values near 2×10 7 cm 2 s −1, 2 days and 18 km were obtained for the diffusivity and the Lagrangian integral time and spatial scales in the along-basin direction, respectively. In the across-basin direction, the statistics are typically 50% of the above values. Geographical and seasonal variations of the Lagrangian statistics can be substantial. It was found that the fluctuating velocities (or the mesoscale eddies) have a preferential cyclonic sense of rotation. The gyres and the coastal currents are mostly prevailing in summer and fall. In winter and spring, they are less intense but the southern one tends to re-circulate more around the South Adriatic Pit. The mean eddy kinetic energy is maximum in winter and fall throughout the central and southern sub-basins. The drifters showed that the southeastward flow along the Italian Peninsula has a width varying between 45 and 70 km and a mean core speed of 25–35 cm s −1. In the northern and central sub-basins, maximum velocities are found within 5–10 km off the coast in winter and spring, while a weaker maximum is seen more offshore (15–25 km) during the other seasons. In the southern Adriatic, the current is wider in summer, fall and winter, whereas in spring, it becomes thinner (maximum core speed near 10 km from shore and width of about 50 km). The maximum core speed is generally larger in summer than in winter.

Turbulence characteristics along the path of a heavy particle

The turbulence along the path of a particle in an isotropic turbulent flow is investigated using direct numerical simulation. The turbulence is simulated using a collocation spectral method on an equi-spaced three-dimensional grid of 128 3 points with a Taylor micro-scale Reynolds number of 65. The particulate phase is treated as a simple system where the flow is not affected by the presence of the particles. A total of 8192 particles are tracked through the flow using a Lagrangian advancement scheme with Stokes drag as the only force applied to the particles. The implementation of the forcing method used to maintain a constant level of kinetic energy within the flow is studied. The total fluid turbulence kinetic energy was found to be a function of particle Stokes number with smaller particles (St<1) seeing slightly higher average velocity fluctuations than a Lagrangian average of the turbulence and intermediate particles (1<St<10) seeing slightly lower average fluctuations. Likewise, the turbulence integral time scales of the fluid along the path of a particle appear slightly larger than both the Eulerian and Lagrangian integral time scales for these intermediate particles. All preferentially concentrated particles (0.1<St<10) saw a lower average vorticity and higher deformation of the fluid than a volume average of the turbulence. The preferential concentration of the particles peaked at a Stokes number of 1 with particles being on average 20% closer to the nearest neighboring particle than in a randomly distributed case. These data suggest that it is the vorticity measured along the path of a particle which is the dominant factor for variations of statistical properties in the particle Lagrangian reference frame.

Lagrangian Covariance Analysis of β-Plane Turbulence

The effects of Rossby wave–turbulence interactions on particle dispersion are investigated in a Lagrangian analysis of the potential vorticity equation. The analysis produces several exact statistical results for fluid particle dispersion in barotropic turbulence on a β-plane. In the inviscid problem the first integral time scale of the meridional velocity is found to be zero, as might occur in pure wave processes, and the meridional particle dispersion is bounded. The second integral time scale, which determines the magnitude of the bound, is shown to depend explicitly on β, the enstrophy and the energy of the meridional velocity. Expressions relating the autocorrelation of the vorticity to the autocorrelation of the meridional velocity are derived and the Lagrangian integral time scale of the relative vorticity is diagnostically related to the meridional velocity correlation. The applicability of these predictions is verified in a series of numerical simulations. For a range of β values, the meridional extent of quasisteady alternating zonally averaged jets occurring in the numerical solutions scales with a length scale given by the the standard deviation of the meridional particle dispersion.

A scalar subgrid model with flow structure for large-eddy simulations of scalar variances

A new model to simulate passive scalar fields in large-eddy simulations of turbulence is presented. The scalar field is described by clouds of tracer particles and the subgrid contribution of the tracer displacement is modelled by a kinematic model which obeys Kolmogorov's inertial-range scaling, is incompressible and incorporates turbulent-like flow structure of the turbulent small scales. This makes it possible to study the scalar variance field with inertial-range effects explicitly resolved by the kinematic subgrid field while the LES determines the value of the Lagrangian integral time scale TL. In this way, the modelling approach does not rely on unknown Lagrangian input parameters which determine the absolute value of the scalar variance.The mean separation of particle pairs displays a well-defined Richardson scaling in the inertial range, and we find that the Richardson constant GΔ ≈ 0.07 which is small compared to the value obtained from stochastic models with the same TL. The probability density function of the separation of particle pairs is found to be highly non-Gaussian in the inertial range of times and for long times becomes Gaussian. We compute the scalar variance field for an instantaneous line source and find good agreement with experimental data.

A skewed meandering plume model for concentration statistics in the convective boundary layer

The meandering plume technique, which assumes that the total plume dispersion can be split into independent meander and relative dispersion components, is especially suited for modelling concentration (fluctuation) statistics in the convective boundary layer (CBL) with its large-scale turbulent motions. We develop a simple and practical meandering plume model for CBL applications that accounts for the skewed and inhomogeneous turbulence characteristics of the convective flow. The meander component is derived from a one-particle Lagrangian stochastic dispersion model by requiring that the meander and relative dispersion components correctly balance the first two total dispersion moments. Balancing of the third total moment implies a skewed relative dispersion, for which a bi-Gaussian distribution is used. The relative dispersion variance is parameterised with an extended asymptotic formulation for travel times much smaller than the Lagrangian integral time scale. For large travel times, the relative dispersion variance approaches the total dispersion variance. The in-plume fluctuations in the relative coordinate system are accounted for via the gamma probability density function. Laboratory data and large-eddy simulation results on total, relative and meander spreads are used to examine the model parameterisations and results. A requirement of the meandering plume model, that it should give the same mean concentration distribution as that obtained by the one-particle Lagrangian approach, is virtually fulfilled. Comparison of the model predictions of the concentration fluctuation intensity with existing laboratory data highlights the important contribution of in-plume fluctuations, which are normally neglected in meandering plume models. The paper also describes limitations of the new model and indicates the scope for further refinements.

Effect of the subgrid scales on particle motion

In this study, the effects of small-scale velocity fluctuations on the motion of tracer particles is investigated by releasing particles in a turbulent channel flow at Reτ=175, and following their motion in time. Two types of numerical experiments were carried out: first, the Eulerian velocity field was evaluated by the direct numerical simulation (DNS) and the particles were advanced in time using the resolved and several filtered velocity fields to study the effect of the subgrid-scale velocity fluctuations on particle motion without the influence of modeling errors. In the second stage, the particle-motion study was performed using independent DNS and large-eddy simulations (LES), thus including the effect of interpolation and subgrid-scale stress modeling errors on the dispersion statistics. At this Reynolds number the small scales were found to have a limited effect on the statistics examined (one-particle dispersion, one-particle velocity autocorrelation, Lagrangian integral time scale, turbulent diffusivity, and two-particles rms dispersion). Only when a significant percentage of the energy was removed from the velocity field some differences were observed between filtered and unfiltered data (especially near the wall). It was found that when the dynamic eddy-viscosity model was employed, modeling errors did not affect the results as much as the filtering itself; the use of the Smagorinsky model, on the other hand, gave inaccurate results. Additional computations for finite-inertia particles have shown that these results represent a conservative estimate, in the sense that actual particles with inertia are less sensitive than the tracer particles examined in the first part of the investigation, and that LES provides improved results when particles with inertia are used.

A Lagrangian Stochastic Model for the Dispersion and Deposition of Brownian Particles

A Lagrangian stochastic model for the dispersion and deposition of submicron-size particles is formulated and validated. The model satisfies the well-mixed condition, incorporates molecular diffusivity, and accounts for the effects of Reynolds number upon Lagrangian particle statistics. Reynolds number effects are found to be significant in the viscous sublayer and the buffer zone of a turbulent shear flow. The effects are due almost entirely to the change in the Lagrangian integral time scale. Sawford's correction to first-order Lagrangian stochastic models for the effects of Reynolds number is found to be appropriate for inhomogeneous turbulence even when the Taylor–Reynolds number Rλ ∼ O(0.1). The model predicts, in close accord with experiment and the results of direct numerical simulations, that the nondimensional particle deposition velocity K+ = 0.06Sc−2/3, where Sc is the Schmidt number. When Reynolds number effects are neglected, K+ is overpredicted by several orders of magnitude.

A Lagrangian dispersion model for predicting CO2sources, sinks, and fluxes in a uniform loblolly pine (Pinus taeda L.) stand

A canopy Lagrangian turbulent scalar transport model for predicting scalar fluxes, sources, and sinks within a forested canopy was tested using CO2concentration and flux measurements. The model formulation is based on the localized near‐field theory (LNF) proposed byRaupach[1989a, b]. Using the measured mean CO2concentration profile, the vertical velocity variance profile, and the Lagrangian integral timescale profile within and above a forested canopy, the proposed model predicted the CO2flux and source (or sink) profiles. The model testing was carried out using eddy correlation measurements at 9 m in a uniform 13 m tallPinus taeda L.(loblolly pine) stand at the Blackwood division of the Duke Forest near Durham, North Carolina. The tree height and spacing are relatively uniform throughout. The measured vertical profile leaf area index (LAI) was characterized by three peaks, with a maximum LAI occurring at 6.5 m, in qualitative agreement with the LNF source‐sink predicted profile. The LNF CO2flux predictions were in better agreement with eddy correlation measurements (coefficient of determinationr2= 0.58; and standard error of estimate equal to 0.16 mg kg−1m s−1) thanKtheory. The model reproduced the mean diurnal CO2flux, suggesting better performance over longer averaging time periods. Two key simplifications to the LNF formulation were considered, namely, the near‐Gaussian approximation to the vertical velocity and the absence of longitudinal advection. It was found that both of these assumptions were violated throughout the day, but the resulting CO2flux error at 9 m was not strongly related to these approximations. In contrast to the forward LNF approach utilized by other studies, this investigation demonstrated that the inverse LNF approach is sensitive to near‐field corrections.